11x^2+14x=-1x^2+48x-24

Solution for 11x^2+14x=-1x^2+48x-24 equation:

11x^2+14x=-1x^2+48x-24

We move all terms to the left:

11x^2+14x-(-1x^2+48x-24)=0

We get rid of parentheses

11x^2+1x^2-48x+14x+24=0

We add all the numbers together, and all the variables

12x^2-34x+24=0

a = 12; b = -34; c = +24;
Δ = b2-4ac
Δ = -342-4·12·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2}{2*12}=\frac{32}{24}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2}{2*12}=\frac{36}{24}
=1+1/2
$